Particle density animation using dynamic texture
Unfortunately, this is a known limitation of the particle system as noted in a bug report here.

To quote Brecht Van Lommel, from that bug report:


  The location of emitted particles are determined in advance now and
  stay fixed, so this can't be animated. There's been some working on
  designing an improved particle system that can handle such animations
  but it's not finished


It is currently listed as a 'To do' item on the development section of the blender wiki here.